Zhongkai Tao

I'm a graduate student at UC Berkeley. I am interested in microlocal analysis. My advisor is Maciej Zworski. My email is ztao@math.berkeley.edu. Here is my CV.

Research

  • Optimal enhanced dissipation for contact Anosov flows, with Maciej Zworski.
  • Appendix to Mathematical results on the chiral model of twisted bilayer graphene, with Mengxuan Yang.
  • Appendix to Classically forbidden regions in the chiral model of twisted bilayer graphene, with Maciej Zworski.
  • Initial data gluing in the asymptotically flat regime via solution operators with prescribed support properties, with Yuchen Mao and Sung-Jin Oh.
  • Counting Pollicott--Ruelle resonances for Axiom A flows, with Long Jin.
  • The fractal uncertainty principle via Dolgopyat's method in higher dimensions, with Aidan Backus and James Leng.
  • Spectral asymptotics for kinetic Brownian motion on Riemannian manifolds, with Qiuyu Ren.
  • Localized initial data for Einstein equations, with Yuchen Mao.
  • Spectral asymptotics for kinetic Brownian motion on locally symmetric spaces, with Qiuyu Ren.
  • Flat trace estimates for Anosov flows, with Long Jin.
  • Exact control for Schrödinger equation on torus from small balls, Pure and Applied Analysis 3(2021), 387-401.
  • On 0-th order pseudodifferential operator on the circle, to appear in Proceedings of the AMS.
  • Talks

    Teaching

  • Spring 2022: Directed Reading Program with Troy Tsubota on differentiable manifolds.

  • Fall 2021: Math 53 Multivariable Calculus.

  • Spring 2021: Math 53 Multivariable Calculus.

  • Fall 2020: Directed Reading Program with Ayush Kamat on measure theory.

    Notes

  • Notes on random perturbation of non-self-adjoint operators, taken from the topics course in Spring 2021 taught by Maciej Zworski.
  • Seminar

  • I organized a learning seminar on fractal uncartainty principle in January, 2022.
  • I organized a learning seminar on semiclassical analysis in spring 2022.
  • I co-organized Harmonic Analysis and Differential Equations Seminar (HADES) with Yonah Borns-Weil and Izak Oltman from fall 2022 to spring 2023.
  • I am co-organizing a learning seminar on orbit method for automorphic forms in fall 2023 with Christopher Dowd and Seewoo Lee.